Not bass, but I did the year long diploma course at the guitar institute (which is now the ICMP) after I left school. It was great and I learned a hell of a lot, but truthfully I wasn't really good enough to be there and I don't think I should have passed the audition in the first place.
Assuming the basic process hasn't changed too much since I was there, I think the most important thing you're going to need is the ability to learn things quickly. I was practising pretty much solidly all the way to bedtime, every day, trying to keep up with all the stuff they were throwing at us, and even then I just got completely snowed under by the end. Constant guitar all day every day burned me out and I didn't play again seriously for almost a year after finishing.
If you decide to go for it, you should give yourself a head start by learning all the theory you can, getting your sight reading up to speed and working hard on your ear training and technique. All important stuff that you'll have to do anyway when you're there, but learning it is pretty mechanical and if you've got it all down by the time you start it will really free you up to focus on the important stuff (i.e. performance, gigging with some good bands and actually putting the theory to work), and you won't be stressing about remembering scales and arpeggios just before you're about to go on stage and start using them! Also have plenty of live experience - I hadn't done all that much when I arrived and it was seriously intimidating having to get up and play a song, unrehearsed, in front of a roomful of musicians who were intensely scrutinising every note!
Also (and again things may have changed) you're likely to be in demand if you're a good player and a quick study. There were never enough bassists to go around when I was there. Tons of playing experience available if you want it .
So it's A LOT of work. Think about whether you're seriously committed to focusing solely on playing music with such intensity (I wasn't, sad as that is to admit), because you won't have time to do much else. The tuition was amazing - at the time, people like Dave Kilminster and Shaun Baxter were teaching there, and having constant access to all that knowledge and experience was just inspiring. I still have really good memories of some of those lessons.
What do you hope to get out of it? Are you looking to turn it into a career?